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NEW YORK — The noise at ground zero is a steady roar. Cement mixers churn. Air horns blast. Cranes soar and crawl over every corner of the 16-acre site.

For years, the future has been slow to appear at the site of the Sept. 11, 2001, attacks. But with six months remaining until the 9/11 memorial opens, the work to turn a mountain of rubble into some of the inspiring moments envisioned nearly a decade ago is thundering forward.

One World Trade Center, otherwise known as the Freedom Tower, has joined the Manhattan skyline. Its steel frame, already clad in glass on lower floors, now is 58 stories tall and starting to inch above many of the skyscrapers ringing the site. A new floor is being added every week.

The mammoth black-granite fountains and reflecting pools that mark the footprints of the fallen twin towers are largely finished, and they are a spectacle. Workers have already begun testing the waterfalls that will ultimately cascade into a void in the center of each square pit.

The memorial plaza won’t be done when it opens on Sept. 11, 2011. But the agency that has been building it is aiming to deliver a memorial experience on the 10th anniversary that closes one chapter — marked by mourning — and ushers in a new one, where ground zero again becomes part of the city’s fabric. “We want people to be able to see that downtown does have this incredible future to it,’’ said Chris Ward of the Port Authority of New York and New Jersey.